The prior art rowing exercise device is generally provided with the oil-pressure cylinders serving as a damping device enabling an exerciser to do a rowing exercise. The cost of making such a rowing exercise device of the prior art is relatively high. In addition, the damping effect of the prior art rowing exercise device can not be adjusted in accordance with the individual requirements of an exerciser using the device. Some of the prior art multipurpose exercise devices are provided with means enabling an exerciser to do the rowing exercise; nevertheless these prior art multipurpose exercise devices are rather expensive and can not be easily adjusted for doing the rowing exercise.